Block #2,096,037

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/1/2017, 5:38:39 PM · Difficulty 10.8718 · 4,718,928 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
f2541f5e3225b15963e219fef92c7498554ed3e8841ae272371140eb995bb9af

Height

#2,096,037

Difficulty

10.871775

Transactions

2

Size

89.73 KB

Version

2

Bits

0adf2ca5

Nonce

1,682,206,239

Timestamp

5/1/2017, 5:38:39 PM

Confirmations

4,718,928

Merkle Root

da1b2c050232f9e0f9ea1b0502fd2aa02fa6ce615f5af8acb20efa7f734a3c9a
Transactions (2)
1 in → 1 out9.4400 XPM109 B
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.231 × 10⁹⁵(96-digit number)
52313675063957135461…84694408725369272319
Discovered Prime Numbers
p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin − 1
5.231 × 10⁹⁵(96-digit number)
52313675063957135461…84694408725369272319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.046 × 10⁹⁶(97-digit number)
10462735012791427092…69388817450738544639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.092 × 10⁹⁶(97-digit number)
20925470025582854184…38777634901477089279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.185 × 10⁹⁶(97-digit number)
41850940051165708368…77555269802954178559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.370 × 10⁹⁶(97-digit number)
83701880102331416737…55110539605908357119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.674 × 10⁹⁷(98-digit number)
16740376020466283347…10221079211816714239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.348 × 10⁹⁷(98-digit number)
33480752040932566695…20442158423633428479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.696 × 10⁹⁷(98-digit number)
66961504081865133390…40884316847266856959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.339 × 10⁹⁸(99-digit number)
13392300816373026678…81768633694533713919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.678 × 10⁹⁸(99-digit number)
26784601632746053356…63537267389067427839
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,763,805 XPM·at block #6,814,964 · updates every 60s
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